Skip to main content
Log in

Mixed intersections of non quasi-analytic classes

Intersecciones mixtas de clases no casi-analíticas

  • Published:
RACSAM - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

Given two semi-regular matrices \( \mathfrak{M} \) and \( \mathfrak{M}' \) and two open subsets Ω and Ω′ [resp. two compact subsetsK andK′] of \( \mathbb{R}^r \) and \( \mathbb{R}^s \) respectively, we introduce the spaces \( \mathcal{E}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) and \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) [resp. \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (K ×K′)]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.

Resumen

Dadas dos matrices semi-regulares \( \mathfrak{M} \) y \( \mathfrak{M}' \) y dos subconjuntos abiertos Ω y Ω′ [respectivamente dos subconjuntos compactosK yK⊥] de \( \mathbb{R}^r \) y \( \mathbb{R}^s \) respectivamente, introducimos los espacios \( \mathcal{E}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) y \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (Ω × Ω′) [respectivamente \( \mathcal{D}_{(\mathfrak{M} \times \mathfrak{M}')} \) (K ×K′)]. En este artículo estudiamos sus propiedades localmente convexas y la estructura de sus elementos, lo que nos ha permitido en [10] obtener representaciones de estos espacios en productos tensoriales y algunos teoremas de núcleos.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Beaugendre, P., (2001). Extension de jets dans des intersections de classes non quasi-analytiques,Ann. Polon. Math.,LXXVI, 214–243.

    MathSciNet  Google Scholar 

  2. Beaugendre, P., (2002).Intersection de classes non quasi-analytiques, Thèse de doctorat, Université de Paris XI, UFR Scientifique d’Orsay,2404, 84 pp.

  3. Chaumat, J. andChollet, A.-M., (1998). Propriétés de l’intersection des classes de Gevrey et de certaines autres classes,Bull. Sci. math.,122, 455–485.

    Article  MATH  MathSciNet  Google Scholar 

  4. Jarchow, H., (1981).Locally convex spaces, B. G. teubner Mathematische Leitfäden.

  5. Schaefer, H., (1971).Topological vector spaces, Springer Graduate Texts in Mathematics,3.

  6. Schmets, J. andValdivia, M., (2005/2006). Extension properties in intersections of non quasi-analytic classes,Note Mat.,25, 159–185.

    MathSciNet  Google Scholar 

  7. Schmets, J. andValdivia, M., (2005). Explicit extension maps in intersections of non quasi-analytic classes,Ann. Polon. Math.,86, 227–243.

    Article  MATH  MathSciNet  Google Scholar 

  8. Schmets, J. and Valdivia, M., About some non quasi-analytic classes, submitted for publication, 24 pp.

  9. Schmets, J. and Valdivia, M., Intersections of non quasi-analytic classes, submitted, 15 pp.

  10. Schmets, J. and Valdivia, M., Tensor product characterization of mixed intersections of non quasi-analytic classes and kernel theorems, preprint, 10 pp.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean Schmets.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schmets, J., Valdivia, M. Mixed intersections of non quasi-analytic classes. Rev. R. Acad. Cien. Serie A. Mat. 102, 211–220 (2008). https://doi.org/10.1007/BF03191822

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03191822

Keywords

Mathematics Subject Classifications

Navigation